BEING CERTAIN WITH UNCERTAINTY

How they measure chance? what are the basic operations in probability? Let us find out.
In tossing of a coin, there are two events-- head and tail. The chance one event occurring = one/total number of events. That is 1/2. You have 50% chance of getting head or tail for each toss. If you toss a coin, one time you should get head and next time you should get tail, so the formula says. But both the times, you may get head or tail. If you toss the coin 100 times, roughly 50 times you will get head and tail. On the long run, the formula proves correct.
On throwing dice, there are six events (1,2,3,4,5,6). Hence chance of getting an 'event' for a throw is 1/6. There are three important logical operations in probability. Let us go for it.

OR operation:
What is the chance or probability getting 1 or 6 in a roll. Here, either 1 or 6 will do for us.
Probability of getting 1 is 1/6
probability of getting 6 is 1/6
Now add both
1/6 + 1/6 =2/6 =1/3
1/3 is the chance of getting 1 or 6. Hence for 'OR' operation, add the probabilities.

AND operation:
What is the chance of getting 1 AND 1 consecutively in two rolls. We know, probability for each event is 1/6.
For AND operation, multiply the probabilities.
(1/6) * (1/6) = 1/36
1/36 is the probability of getting a one AND a one, one after the other. 1/36 is a very small number. Hence the occurrence of the event is rare and unlikely.

NOT operation:
What is the probability of NOT rolling a six. That is, we may get 1,2,3,4,5 but not 6. The total probability is always '1'. The probability of rolling 6 is 1/6. Now subtract 1/6 from 1
1-1/6 = 5/6
5/6 is the probability of rolling 1 or 2 or 3 or 4 or 5 and NOT 6. 5/6 is large value. Hence 'Not throwing 6' is very likely to happen.

By combining the three logic operations in various ways, we can answer many questions. For example: if you are dealt five random cards from standard deck of 52, what are the chance of getting one pair whose values match(a pair queen or a pair of A ) and no other matching cards? It is left to the reader as a home work!

FOOT NOTE: Using the same three logic operations and binary numbers, computer is able to do miracles. So does the probability theory.
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